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%I #18 Nov 09 2022 22:05:52
%S 10917,11527,50923,73894,111468,118436,128662,139123,195234,249281,
%T 332863,435489,438080,482557,538373,542299,650254,679958,722145,
%U 803501,810871,820409,962582,970711,1003544,1027732,1030010,1190134,1204929,1305603,1636065,1689410
%N Numbers k with property that the sum of 120 successive primes starting with prime(k) is a square.
%C Corresponding values of s = sqrt(Sum_{i=k..k+119} prime(i)) are A166262.
%e a(1) = 10917: Sum_{i=0..119} prime(10917+i) = 3734^2 = A166262(1)^2,
%e a(2) = 11527: Sum_{i=0..119} prime(11527+i) = 3846^2 = A166262(2)^2.
%t PrimePi/@Select[Partition[Prime[Range[169*10^4]],120,1],IntegerQ[ Sqrt[ Total[ #]]]&][[All,1]] (* _Harvey P. Dale_, Jan 22 2019 *)
%o (PARI) lista(nn) = {pr = primes(nn); for (i=1, nn-119, s = sum(k=i, i+119, pr[k]); if (issquare(s), print1(i, ", ")););} \\ _Michel Marcus_, Oct 15 2013
%o (PARI) S=vecsum(primes(119)); p=0; q=prime(120); for(n=1,oo, issquare(S+=q-p) && print1(n","); q=nextprime(q+1); p=nextprime(p+1))} \\ It is about 25% faster to avoid "nextprime(p)" at expense of keeping the last 120 primes used in a vector p, using {my(i=Mod(0,120)); ...p[lift(i)+1]... i++}. - _M. F. Hasler_, Jan 04 2020
%Y Cf. A166262.
%Y Cf. A064397 (2 primes), A076305 (3 primes), A072849 (4 primes), A166255 (70 primes).
%K nonn,less
%O 1,1
%A _Zak Seidov_, Oct 10 2009
%E a(30)-a(32) from _Michel Marcus_, Oct 15 2013
%E Edited by _M. F. Hasler_, Jan 04 2020
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